Peter Collins is from Ireland. He retired recently from lecturing in Economics at the Dublin Institute of Technology. Over the past 50 years he has become increasingly convinced that a truly seismic shift in understanding with respect to Mathematics and its related sciences is now urgently required in our culture. In this context, these present articles convey a brief summary of some of his recent findings with respect to the utterly unexpected nature of the number system.

Integrating Structuresand States

Part One

Peter Collins

In dynamic terms all stages represent the interaction of both structures and states. From an integral perspective both of these aspects are fully complementary with each other with the most scientific appreciation of their relationship provided through holistic mathematical interpretation.
This article attempts to clarify other important features that are generally neglected e.g. confused and mature experience of both structures and states, the distinction as between "day" and "night" use and the various ways in which both peak and valley experience can occur.

Defining Structures and States

In dynamic terms every stage of development expresses the interaction of both structure and state aspects.

Structures and states can be defined in various ways so it is important in this context to clarify the manner in which I use the terms.

In the primary sense, a structure relates to the fundamental holistic manner in which each stage of development is phenomenally configured (with attention in these articles on the 12 major levels).
Once again my basic contention is that all primary structures are inherently mathematical (in a holistic sense). So for example the most advanced stage (R3) is configured in terms of both the mature linear (differentiated) and circular (integral) development with respect to the three fundamental polarities (horizontal, vertical and diagonal).
Therefore from this perspective, primary structures are synonymous with such holistic mathematical understanding providing the most appropriate scientific interpretation of their universal nature.

We can distinguish as between a primary structure defining the holistic nature of a stage and secondary expressions representing various arbitrary phenomenal manifestations of this structure.

For example I would see the major mystical traditions as mainly expressive of secondary structures with respect to the higher levels.
Though Christians and Buddhists for example might choose to express experience of the higher stages through appropriate secondary structures associated with their respective traditions, mutual agreement as to the truly universal features of these stages properly requires the holistic scientific appreciation of their primary nature (which ultimately is mathematical).

We can also distinguish as between primary and secondary states.
A primary state relates to the fundamental holistic pattern of spiritual "seeing" which once again is uniquely defined for each stage.
Though the conventional terminology of waking, dream and deep sleep do indeed refer to primary states, such language is not sufficiently universal and lacks coherence from an overall scientific perspective.
Thus, though the primary states apply to all holons, in conventional usage, waking, dream and deep sleep are confined merely to human (and animal) holons. Therefore there remains an important need to interpret primary states in a manner that is truly universal.
Also when properly understood in integral terms, states and structures are fully complementary, with the state relating to the holistic pattern of "seeing" (as emptiness) and the structure relating to the corresponding pattern of what is thereby phenomenally seen (as form).
However once again this is not at all apparent from customary understanding, which thus leads to considerable confusion with respect to the matching of (primary) states with corresponding (primary) structures.
Secondary states relate to the physiological, affective, cognitive and volitional ways through which the primary nature is expressed.[1] Altered states would largely relate to secondary expression (in my terminology). For example one could have an artificially induced temporary experience of "higher" stages through drink or drugs. However we would then need to distinguish the manner in which the underlying primary states (waking, dream and deep sleep) are affected through the physiological and psychological changes thereby triggered.
A more authentic - and sustainable - experience of the "higher" levels could arise through meditative practice. However this altered state is still secondary in that it relates to a particular expression of the underlying primary aspect (i.e. dream or deep sleep).
Thus for example, the spiritual illumination which characterises the mature dream state of the psychic/subtle level (H1) can be indirectly manifested through a variety of secondary states.

It might help initially to think of a (primary) state in more personal terms i.e. as a general (empty) spiritual disposition associated with each stage. A (primary) structure would then be identified in a more impersonal manner as the unique configuration (of form) with respect to the stage identifying its fundamental nature. [2]

We could also define a state in psychological terms as representing a certain configuration in the relationship of both conscious and unconscious understanding.
Thus the deep sleep state relates to experience that is defined largely by the unconscious; at the other extreme the waking state pertains mainly to the conscious aspect with the dream state then entailing a greater interaction of both conscious and unconscious. (However in practice - as we shall see - these various states can dynamically overlap in unexpected ways).

We would then define the corresponding structure in philosophical terms as representing a certain configuration in the relationship of both linear and circular understanding. Thus - as we shall see in accordance with the holistic digital binary system - every stage has a unique structural configuration defined by the precise interplay of linear (differentiated) and circular (integral) aspects.
Thus linear and circular aspects (as structures) directly correspond with conscious and unconscious aspects respectively (as states).

Even more remarkably the holistic binary digits i.e. 1 and 0 - which can be potentially used to configure the structure of every stage - correspond exactly with dynamic on-off states that can be used in like manner to configure the primary states associated with each stage of development.

So once again, each stage is fundamentally defined in dynamic terms as representing the unique interaction of both (primary) state and structure aspects.

For example the middle level is defined by the waking state, which in the context of this stage enables us to consciously "see" from this stage perspective. It is equally defined by its corresponding linear asymmetric structure enabling us to rationally interpret what is thereby phenomenally "seen". And both aspects mutually support each other. So the waking state facilitates the use of rational structures; equally such use of rational structures facilitates in turn the waking state. (Not surprisingly therefore too much thinking tends to keep one awake at night!)

Though states and structures have - relatively - distinct independent identities (in terms of differentiated understanding), they also necessarily interact both within and between levels from an integral perspective.

Indeed properly understood from this integral perspective, states and structures are ultimately fully complementary with each other (though at certain stages of development they are largely understood in discrete terms).

In a balanced treatment (i.e. radial) we must allow - where appropriate - for both the discrete differentiated interpretation of states and structures (where they are understood as largely separate) and the continuous integral view (where they are seen as mainly interdependent).

Confused and Mature Expressions

We can likewise identify states i.e. waking, dream, deep sleep and nondual (as eternal emptiness) with respect to both their confused and mature expressions. In general what - in discrete terms - are often referred to as the prepersonal stages, entail the confused expression of these states whereas the transpersonal entail the corresponding mature experience. In this sense prepersonal and transpersonal stages are complementary with each other in dynamic terms (with respect to states). In early development interaction leads to a confused experience of both aspects (i.e. pre and trans) though they are necessarily intertwined. With advanced spiritual development again both aspects interact closely (now experienced in mature manner).
In similar fashion, we can identify structures i.e. linear, wavelike, circular and nondual (as ultimate form) with respect to both their confused and mature expressions, with once again the prepersonal corresponding to confused and transpersonal to mature versions of these structures respectively.
Indeed despite the looseness of conventional terminology, I will demonstrate later how each of the 12 major levels has unique matching state and structure configurations.

Day and Night Understanding

However we need to make another important distinction, which is often overlooked, in what we might call the day and night use of both states and structures.

Let me explain.

In conventional terms, we tend to separate sleep and waking aspects in a discrete manner. So the conscious is predominantly associated with (day) waking activity whereas the unconscious is likewise associated with (night) sleep.
And in a society that is largely geared towards conscious understanding, much greater attention is thereby placed on (day) waking activity.

Indeed because this understanding (on which such activity is predominantly based) does not formally recognise dynamic links as between the waking state and its corresponding structures, this means in effect that conventional understanding is largely geared to the structural interpretation of the middle levels.
It might be accepted for example that one needs to be awake to understand a (rational) scientific hypothesis. However because the waking state is considered neutral with respect to corresponding structures, this means in effect that (conventional) scientific truth is identified solely with the structural understanding of its corresponding stage (i.e. the middle level).

Whereas - as explicitly interpreted - the relation of the middle level structure is formally neutral with respect to its corresponding state, this is not true of any of the other levels. Here states and structures interact in a dynamic manner thereby continually changing the very nature of understanding associated with these levels.

However - using conventional discrete terminology - though it appears true that day activity is characterised by the waking (conscious) state, strictly this is not true from a dynamic perspective.
In other words actual “waking” activity (or wakefulness) necessarily entails the dynamic interaction of both conscious and unconscious aspects of personality.

It is not possible therefore to experience a pure waking state. Indeed there are clues as to this given in normal language.
One can for example fantasise and “daydream” (while conventionally awake). Also when not paying attention one might be accused of being “asleep” (though again conventionally awake). In other words one can screen out conscious attention - and in this respect be unconscious to certain stimuli - while awake.

Therefore - though the conscious aspect of experience may indeed predominate - wakefulness, in dynamic experiential terms, is characterized by the interaction of a variety of states (i.e. waking, dream and deep sleep) even while the conscious aspect is dominant.
Likewise in corresponding structural terms, though normal (day) activity may well be dominated by the rational understanding of the middle stages, actual experience will necessarily entail varying interacting configurations of lower, middle, higher and radial structures.

Thus in this context it is not strictly true - as Ken Wilber maintains - that the waking state supports a variety of structures.
The fact is that wakefulness - what we conventionally call the waking state - represents a dynamic configuration of several states. Likewise though the rational may indeed dominate, the associated experience comprises a dynamic mix of several structures. So in dynamic terms these states and structures are interdependent and mutually support each other.

Likewise though in conventional terms, we associate (night) rest with unconscious sleep, in dynamic terms both conscious and unconscious are necessarily involved (though again the unconscious aspect may predominate).
Conventional sleep is also normally associated with dream activity (where conscious and unconscious interact). However - though less common - it can equally be associated with lucid conscious activity.

Therefore - what we conventionally refer to as sleep - can potentially be associated with all states (though the unconscious aspect normally is primary).

Equally from the structural perspective, conventional sleep activity can potentially be associated in varying configurations with all stages of understanding (prepersonal, personal, transpersonal and radial).

It is very important to make this distinction as regards - what I conveniently refer to as - day and night experience.
In other words there is both a day and night experience of the stages of development where in each case states and structures (and structures and states) interact in dynamic manner.

For example when we consider the extent to which one can obtain peak access to higher stages, while habitual experience is customarily at a lower level, it is important to distinguish the day from its nighttime counterpart.

Now insofar as such peak experience occurs, the dynamic complementarity of levels is especially relevant.
Therefore one tends to peak the "higher" from the corresponding "lower" level (with which it is complementary).

The very definition of stages in discrete terms entails that appropriate differentiation has already taken place. However in the context of earliest infant development this makes little sense. So the clear differentiation of "lowest" and "highest" has no meaning at this time. Thus what we may later identify in discrete terms as the earliest stage - L3 in my terminology - in earliest development is directly confused with what later is identified as the highest stage (i.e. H3).
Thus in earliest development at L3 (before differentiation of structures properly unfolds), one has continuous access (in a greatly confused fashion) to the corresponding "highest" level of H3.
As appropriate differentiated development proceeds, one loses this capacity for such continual access (in confused manner).
However though access now becomes more temporary, the possibility of occasional lucid moments arises.

Though in theory it is possible to have lucid experience of "higher" from any of the "lower" levels, in general this would be more probable with respect to stages close to the middle level (where sufficient differentiation of structures to sustain such moments may already have unfolded).
And such differentiation will be identified more with the day rather than the nighttime experience of the stage.
Thus in practice, temporary peak moments of lucid spiritual awareness are most likely to occur in terms of day experience of L1 (mythic) relating to its complementary "higher" level i.e. H1 (subtle).

As mentioned on many previous occasions such peak moments can occur with respect to both states and corresponding structures. Indeed in dynamic experiential terms, both aspects must necessarily be involved. However the precise balance can vary considerably so that sometimes the state is dominant (and in other cases the structure).

For example one could peak from L1 (mythic) a unique experience of spiritual illumination associated with the complementary "higher" psychic/subtle stage (H1).
In this case the (primary) state would predominate though it would necessarily be indirectly expressed through the medium of the corresponding (primary) structure of the level.
However one could also in a peak moment of inspiration - say at L1 - attain lucid knowledge of intellectual concepts (associated with H1). [3]
In this case the (primary) structure would predominate in experience though supported indirectly by the corresponding (primary) state giving rise to the concepts.

Indeed "higher" level development can be either led by states or structures.
Where too much attention to states is in evidence considerable dynamic fluctuation as between stages can take place making it thereby difficult to consolidate the corresponding structural understanding of the stages. [4] However with too much concentration on the appropriate structures of a given level, experience tends to plateau at this level thereby reducing dynamic access to all levels.
Indeed the key reason why so few in our society gain permanent access to the "higher" (and radial) levels is due to the fact that the understanding of the middle stages - which defines accepted conventional appreciation of reality - is largely based on the mere structural interpretation (associated with these stages).
Therefore successful development with respect to both the heterarchical and hierarchical aspects of all stages requires that appropriate dynamic balance be maintained as between the structures and states associated with each stage.

There is often an unfortunate tendency in spiritual writing - especially with respect to Eastern type understanding - to deal with the "higher" levels predominantly in terms of states and then to misleadingly identify the permanent attainment of these states as their corresponding structures.
Indeed I would see this as a major weakness with respect to Ken Wilber's writings. Here I can find little or no recognition of the (primary) structures associated with more advanced levels.
So once again - especially in cognitive terms - Ken attempts to marry "higher" states with the middle level structural understanding of vision-logic leading to an integral translation of development that is intellectually reduced and inconsistent.
However this is not sustainable. For example at the middle levels we can identify the waking state and its important cognitive rational structures e.g. conop, formop and vision-logic.
However we cannot equate the permanent attainment of the waking state with these structures.

Likewise at H1 (subtle level) we can identify the spiritually illumined nature of the (mature) dream state. However - as at the middle level - this state is associated with its own distinctive forms of phenomenal structures - cognitive, affective and moral. These are circular and bi-directionally interactive in nature (based on Type 1 complementarity). Indeed - as I have frequently demonstrated - the proper use of the cognitive aspect of such structures is the minimum required for an appropriate integral (i.e. Integral 1) intellectual interpretation of development.

Unfortunately we are provided with no true clarity on these corresponding structures in Ken Wilber's writing. Indeed he frequently gives the impression that the most advanced level of cognitive understanding occurs with the vision-logic of the centaur (beyond which lie - merely - transpersonal spiritual states).

However from my perspective I would see this as very mistaken and symptomatic once again of the lack of an appropriate interactive approach to development.
Also by attempting in this context to identify the dynamics of experience with fluctuations in states, he is enabled to maintain rather rigid notions regarding his basic structures.

For example Ken would maintain that once formed, the basic nature of formop does not change though admittedly appreciation of this structure may continually develop.

However from a dynamic perspective this conclusion is unwarranted.

Indeed properly understood (in dynamic terms), we have a whole range of enhanced interpretations of formop (from the perspective of the more advanced stages - higher and radial) where its very nature does indeed continually change.
In this sense formop (and in like manner every other basic cognitive structure) is in continual transition throughout development.

Perhaps I can throw some light on what I see as a possible reason for Ken's failure to properly recognise the existence of unique distinctive cognitive structures at the "higher" levels.

However because he looks at stages in a somewhat sequential asymmetric fashion, from this perspective it implies that it would be even more difficult to peak the structures of a higher level (from a lower stage).
Therefore, recognising the strong evidence that temporary peak experience of the higher transpersonal levels is indeed possible for one habitually experiencing at lower levels, he concludes that such temporary experience is of states (rather than basic structures).

However in dynamic terms the circular complementary approach to stages is especially relevant in terms of explaining the nature of peak temporary access.
In other words - because of the complementary relationship between "lower" and "higher" - we peak stages that are defined largely in complementary (rather than sequential) terms.

For example as we have seen, L3 (archaic) is most complementary with H3 (nondual). Thus the primitive experience of the newly born infant represents in interactive terms - literally - the dynamic confusion of both these levels, which are pre and trans (and trans and pre) with respect to each other. Thus what we identify in discrete unambiguous linear terms as the first level (L3) more correctly - from a dynamic perspective - represents the very close interaction of L3 and H3 (in a greatly confused manner).
Likewise in dynamic terms, L2 (magic) peaks H2 (causal). However once again as little differentiation of structures would not yet have occurred at the magic stage, this is likely to be of a very confused nature.
Then L1 (mythic) peaks H1 (subtle). Here, temporary peak moments of lucid spiritual experience are much more likely, especially in a daytime context, due to the greater degree of differentiation of structures now obtained.

However as we have seen, the middle level (initially) is complementary with itself.
Therefore - as there is very limited dynamic access possible from the "lower" to the middle level - this explains why it is not usually possible to peak the structures (especially more advanced) of the middle level from earlier stages.

Of course peak transpersonal experience of "higher" stages is still actually possible at this level.
However strictly speaking, this is because - in dynamic terms - the middle does not achieve full specialisation and necessarily remains in dynamic interaction with other levels (especially "lower").
This thereby provides an enhanced experience of L1 (mythic) and - to a lesser degree - L2 (magic) enabling a better quality of complementary interaction of these with corresponding "higher" levels.

Peak and Valley Experience

However once we accept the dynamic complementarity of stages, then it is easy to accept that temporary peak access of "higher" structures (as well as "higher" states) can occur from corresponding "lower" levels.

Indeed this realisation indeed could be helpful in facilitating recognition of the vitally important fact that we do indeed have very important distinctive basic structures of form at each of the "higher" (and radial) levels.
Indeed we can distinguish at least three types of peak access of "higher" from "lower" levels.

This represents the continual confused access at early infancy of the "lowest" (L3) with the corresponding "highest" stage (H3). Because so little differentiation has yet taken place in experience, prepersonal and transpersonal cannot yet be meaningfully separated. So both pre and trans (and trans and pre) are therefore still entangled with each other in a greatly confused fashion.

As differentiation proceeds through the lower levels, continual (confused) access with the higher levels gradually diminishes. However the possibility now arises of occasional moments of peak awareness (of a lucid kind) with respect to the higher stages. Though in theory these could occur at any stage, more realistically they are likely to take place at the mythic (L1) relating to its complementary psychic/subtle stage (H1) where a sufficient degree of differentiation to support such temporary access is more likely to have taken place. However such moments cannot be properly sustained and tend to be dissipated on return to the customary interpretation of the lower stage.

The most interesting of childhood experience relates to the possibility of occasional peak moments of extraordinary lucid awareness of the "higher" levels which can subsequently have a considerable transforming spiritual effect on personality. These are most likely with those who have a latent talent for mystical development, who even at an early age can feel set apart from conventional life.

Thus when these peak mystical moments occur they are so intense that one realises on return to the customary level that it cannot adequately incorporate the nature of the experience. Thus considerable dissatisfaction with this lower stage can arise as one unconsciously seeks to recapture those peak moments of meaning. Therefore in appropriate cases, they can act as a considerable catalyst in accelerating spiritual development in the personality.

It has long been my belief that the true intellectual task for our age is in the gradual unravelling of the full nature of the more advanced structures and their corresponding dynamic application to all transformation processes.

So emptiness (as spiritual states) is always related to form (as phenomenal structures) and likewise form is always related to emptiness. Therefore it is vital for balanced understanding of development (especially with respect to "higher" stages) to maintain this two-way interaction of structures (form) with states (emptiness).

However just as we can peak "higher" stages from (complementary) "lower" stages (with respect to states and structures), equally we can have valley experiences of "lower" stages from the perspective of the habitual experience of "higher" levels.

Thus it is important to point out that even for those with normal continual access to the "higher" levels, that temporary confused valley experience of "lower" levels is very likely.

Again we can distinguish three types of this "valley" experience.

Just as we have normal confused access to the "highest" level (H3) from the "lowest" level (L3) in early development, likewise - in reverse manner - we have the normal mature access from the "highest" level (H3) to the "lowest" (L3) with advanced contemplative development. [5] This relates to the two-way integration of the Spirit with the body and - in reverse manner - the body with the Spirit.

However just as there can be temporary peak moments of lucid awareness - especially from the "lower" mythic (L1) to the "higher" subtle level (H1) - equally there can be temporary valley moments of confused prepersonal awareness in the corresponding reverse direction from H1 to L1.
Thus for example one who has truly attained to the subtle level of spiritual awareness (and even beyond) may still occasionally interpret such experience in a (confused) mythical manner. [6]

The most interesting - though also most disturbing case - arises with confused valley experiences of extraordinary force that can subsequently lead to the corruption of mystical awareness already developed.

One manifestation of this is in succumbing to the worldly temptation to use the immense spiritual power that comes with such development in a self-serving manner.

In using the terminology of waking, dream and sleep states, Ken characteristically identifies them with the gross, subtle and causal realms respectively.
He then sometimes appears to maintain that - because all humans (including children) have access to these three states - they thereby provide (especially in terms of dream and deep sleep) a natural gateway to the transpersonal experience of these realms.
However if held this would represent faulty thinking stemming I believe from a faulty classification of states. [7]
It is quite valid to maintain that waking, dream and (deep) sleep constitute three primary states (which with the inclusion of the nondual eternal) would give us four in total.
However Ken does not properly clarify that these states have both confused and mature expressions.
Thus whereas the "higher" levels i.e. H1 (subtle), H2 (causal) and H3 (nondual) represent the mature developed spiritual expression, their complementary "lower" levels L1 (mythic), L2 (magic) and L3 (archaic) represent the corresponding confused material expression of these same states. Therefore in this sense, L1, L2 and L3 represent the confused expression of the subtle, causal and nondual realms respectively. [8]

However the proper recognition of this fact would immediately entail that the prepersonal stages are necessarily in continual dynamic interaction with transpersonal (and transpersonal with prepersonal). So any clear separation of pre and trans (and trans and pre) is strictly meaningless in this context. This would then pose major problems for Ken's limited formulation of the pre/trans fallacy.

Thus a child normally does not have access (even on a temporary peak basis) to the mature transpersonal domains through deep sleep or dream activity (considered in the conventional nighttime context).
As we have seen, the lucid mediation of the spiritual implicitly requires a necessary development in differentiated structures (to effectively support the state). However whereas this might indeed be possible during normal (day) waking - especially at the mythic level of development - it is much less likely during (night) sleep activity. Because experience is here naturally biased towards the unconscious, there is a considerable dampening down of conscious faculties (thereby rendering it unlikely that lucid experience can occur).

However lucid spiritual activity can certainly occur during (night) activity when conscious structures are properly developed.
Indeed in such cases spiritual experience can occasionally unfold more easily during night rather than day activity.

Lucid spiritual awareness requires the creative interaction of both conscious and unconscious aspects. Because in our culture the unconscious is inhibited during daytime affairs (due to considerable emphasis on the specialised conscious aspect), this implies that the unconscious frequently attempts to exercise a compensating balance during nighttime. This can lead - especially in the context of a deep search for true existential meaning - to archetypal spiritual revelations at such times.
In other words the holistic pattern that provides meaning to disparate conscious aspects (in day terms) can be creatively provided through (night) dreams.

In the Christian Bible there is considerable emphasis on dreams as a means of spiritual revelation. Often this is symbolised through the appearance of angels.
The word "angel" means messenger. Such apparitions therefore reflect spiritually important messages that are revealed through the unconscious.

So to sum up:
When properly understood in integral terms, states and structures (and structures and states) are fully complementary with each other.

We can peak the temporary experience of a more advanced level from the corresponding lower level (with which it is complementary). However it is important to recognise that such peaking can take place both with respect to structures as well as states. Thus we can have temporary peak access to both "higher" level structures and states from corresponding "lower" levels.

Equally - and very importantly - we can have temporary valley access to both "lower" level structures and states from corresponding higher" levels".
Then when the development of a particular stage has been sufficiently consolidated we have more permanent access to both the (primary) structures and states of that level.
Thus it is somewhat confusing - and ultimately very misleading - to identify the permanent attainment of the (primary) state of a "higher" level with its corresponding structure. So once again I would find Ken Wilber's treatment of the more advanced levels of development as greatly lacking in the proper clarification of the (primary) structures of these levels.

And, as an appropriate integral account of development - that is properly consistent in intellectual terms - is intimately based on use of the (primary) cognitive structures of the "higher" stages, this indeed is a very major shortcoming.

Bridging the Dualistic Divide

An interesting view on the nature of advanced spiritual development can arise from seeing it as a means of fully bridging the (dualistic) divide as between day and night experience.

As befits a bi-directional approach we can look at this in complementary opposite terms.

Therefore from one perspective we can see it as an attempt to render conscious (day) activity fully unconscious (while conventionally awake).
Equally from the other perspective it can be seen as the attempt to render unconscious (night) activity fully conscious (while conventionally asleep).

In this way one aims at achieving the dual paradox of being able to deeply sleep (while remaining conventionally awake) and likewise remaining fully awake (while conventionally asleep).
Put another way when this double state is realised, all (dualistic) boundaries as between "fantasy" and "reality" disappear. What seems "real" (in conscious) terms is understood as but maya (illusion) from a deep spiritual (unconscious) perspective. Likewise what is "fantasy" in conscious terms is seen as truly "real" (in spiritual archetypal terms) from the corresponding unconscious perspective.
So here conscious and unconscious aspects mutually interpenetrate (without rigid distinction).

In fact we can distinguish four aspects to this daytime/nighttime paradox.

The word "night" (for example with St. John of the Cross) is used to symbolise the deep spiritual development of the unconscious.
This in turn requires the gradual detachment from all (rigid) conscious phenomena.

Thus when this (unconscious) spiritual development reaches its full maturity at H3, conscious phenomena no longer remain in memory.
One can still attend to day activities but with a detached conscious mind that does not evoke any conscious light (through phenomenal stimuli). Therefore one's (day) affairs are conducted as if sleepwalking (or more accurately sleepwaking).
So while one remains conventionally awake the conscious mind largely closes down during this time (enabling the unconscious achieve profound spiritual growth).

Closely associated with this deep sleep state at H3 (while conventionally awake) is a waking state (while conventionally asleep). In other words one can relax into restful sleep while remaining on the threshold of consciousness. It is somewhat like the sleep mode on a computer. As soon as a key is depressed the screen is on again. Likewise here as soon as a slight external stimulus is applied e.g. being spoken to, one is immediately able to respond (as if awake all the time).
So just as the other state represents sleepwaking, this represents in reverse wakingsleep.
In both cases it is associated with considerable economy of conscious effort (so as to facilitate pure specialised growth of the spiritual unconscious).

However on the other side of H3 i.e. radial stages, we have the gradual unfolding of the opposite direction whereby what is unconscious is now made fully conscious.
In other words the spiritual energy that has incubated in the unconscious (in a state of deep sleep) is now transferred to the conscious mind as a full awakening in Spirit.
However paradoxically, while fully awake (in pure conscious terms) equally one can remain in deep sleep in the depths of personality (due to the relationship already established with the unconscious). Indeed it is this integral contact with the unconscious that enables the greatest practitioners to continually screen out (rigid) attachment to phenomena even when intensely active (in conscious terms).

From the other perspective one can remain fully conscious (now in an active manner) while conventionally asleep.
For example one now has the capacity for lucid reflection on issues (while conventionally asleep). This can often result in a greater clarity of insight (that when in the conventional waking state). So now one is bringing the conscious - as it were - fully to bear on the unconscious mind.

Nature of Visions

Again in the context of my religious tradition (Christian) I have long been fascinated by the phenomenon of visionary experience. Here an important religious figure e.g. Christ, his Mother or - in recent times perhaps the Italian friar Padre Pio - can appear in bodily form often heralding a dramatic spiritual transformation in the witness.

Now such visions can be appropriately explained in terms of experience that lies very close to the threshold of both the conscious and unconscious and thereby able to participate simultaneously with respect to both aspects. [9]
So these can fruitfully be represented as a special kind of sleepwaking experience.
Therefore from one perspective one is still consciously awake and clearly able to register phenomena e.g. one's surroundings, the time etc. However equally one is participating in a deep sleep (or trance like) state where the unconscious is given free expression.
Therefore given the appropriate circumstances, one can in such states freely create (from unconscious desire) images or apparitions of people that are accurately embodied in "real" world surroundings.

Not surprisingly such images - literally - appear "real" while they are being experienced.
However their true significance lies in the profound archetypal meaning (expressive of the spiritual unconscious) that they can embody.

For the spiritual disciple, such apparitions sometimes arise at key transition moments of development carrying an important sign (or perhaps several signs) regarding one's future course of development.

Integral Mathematical Nature of States and Structures

When looked at from a personal perspective, we can identify 3 fundamental states applicable to humans (and indeed animals) i.e. waking, dream and deep sleep.
Indeed waking and sleep are the vital states here (with dream entailing a composite interaction of both)

Likewise when looked from the impersonal perspective we can identify 3 corresponding fundamental structures that are equally applicable i.e. differentiation (corresponding to waking), integration corresponding to deep sleep and the interaction of both aspects (differentiation and integration) corresponding to the dream state. [10]
Not surprisingly in this context the movement from the waking to the mature dream state H0 (centaur) - H1 (subtle) corresponds with the movement in structural terms from differentiated to (spiritually) integrated understanding.

So from a more balanced perspective we have three fundamental states that are matched by three fundamental structures.

Indeed in the manner in which conventionally expressed, we could argue that the structures are even more fundamental that the states.

Thus whereas differentiation, integration and the interaction of both necessarily apply to all holons, waking dream and deep sleep have a less general application (being largely confined to humans and animals).

Thus to provide a more universal scope for states we must redefine them in such a manner as to be generally applicable to all holons.
Now the simplest way of doing this - using computer terminology - is in terms of on and off (and the interaction of both off and on) states.

Thus the on state refers to a dualistic capacity for form (which every holon must possess). The off state then refers to a nondual capacity (i.e. relationship to emptiness) and the on-off (and off-on) state refers to the interaction of dual and nondual aspects.

Now we can see a fascinating scientific correspondence with structures (through the use of holistic mathematical language).

So differentiation, integration and the interaction of both can be referred - in holistic mathematical terms - as linear, circular and spiral (or wavelike) structures.

This in turn represents the holistic binary system as 1 (linear) (0) circular and the dynamic interaction of 1 and 0 (i.e. spiral) structures.
As we know in electronic terms the analytic binary system is represented by on and off states with respect to electronic circuits.

So once again we can perhaps see the great power of the holistic mathematical approach.

Thus from an analytic mathematical perspective, all information can be potentially encoded (as structure) through the binary digits 1 and 0. This can be electronically represented in turn by on-off switching (as states).

Notes

1. For example drunkenness would relate to a physiological secondary manifestation through which the primary states of waking, dreaming and perhaps deep sleep could be expressed (generally in a very confused manner).
As we all know there are degrees of drunkenness. A person could be moderately drunk yet sufficiently awake to have an intelligent conversation say on the political happenings in a country. However the same person might not be sufficiently awake to drive a car safely. So here the confused "dream" aspect of the state would be likely to impair rational judgement. And of course if a person is sufficiently drunk a condition of total stupor will eventually result relating to the (confused) deep sleep aspect.

The feeling of joy following for example a special spiritual illumination could represent a secondary affective expression of the dream state.
A disciplined approach to spiritual meditation could then represent a secondary cognitive expression of the (primary) dream or perhaps deep sleep state.
The continual good intent (in the desire for spiritual truth) could finally characterise a secondary volitional expression of the various primary states.

Secondary structures can be of a deep or more superficial nature. The core teachings of the mystical religions would be expressive of deep (secondary) structures in various ways (which however are not generally properly distinguished from states). A particular practice - say the prohibition on certain forms of dress - would represent a corresponding superficial (secondary) structure in this context.
Primary structures are always of a deep nature. What distinguishes them from secondary is their truly universal scientific character (which ultimately is mathematical in a holistic sense).
Thus the Bardo teachings, which Ken Wilber uses with respect to his involutionary realms, relate to secondary rather than primary structures and in this sense are not sufficiently scientific for a truly general theory of development.

2. Because states and structures are truly interdependent in integral terms, ultimately they cannot be dualistically separated. So every structure has a corresponding state aspect and every state has a corresponding structure aspect. As shown in previous articles, in holistic mathematical terms every "real" structure has equally an expression as an "imaginary" state and every "real" state likewise an expression as an "imaginary" structure. This means in effect that to switch from conscious recognition of a structure to a state, we must render the structure unconscious; likewise to switch from conscious recognition of a state to a structure, we must render the state unconscious. And when experience becomes very refined in spiritual terms, these two processes tend to occur almost simultaneously.

3. With respect to my own experience I have had a long fascination with imaginary numbers and had a very clear insight at an early age that their philosophical secrets could only be unveiled in terms of a different logical system. This represented therefore - I believe - an especially lucid temporary peak experience of the structure of a "higher" stage. Now of course, I would not have been able to express the insight in an acceptable intellectual fashion at that early age. However with the benefit of the enhanced interpretations of earlier (provided through more advanced) stages I would now be better able to articulate the nature of this key revelation which had a subsequently major transforming effect in my whole approach to mathematics.

4. I have mentioned before how Evelyn Underhill in "Mysticism" highlights the experience of Madame Guyon as a good example of mystical progress that was largely dictated by the predominance of fluctuating states (without sufficient corresponding structural development). Though much better integrated, the mystical development of Teresa of Avila would also represent the same phenomenon to a lesser degree.

Though by no means a universal feature it does seem that the "emotional" mystic is more likely to follow a states led course of mystical development, with the "intellectual" mystic following a more structurally defined approach.
Thus the great philosopher Hegel strikes me as one who had initial genuine spiritual access to the "higher" levels but whose subsequent contemplative development was impaired through an over reliance on the structural formulations of these stages.

5. Strictly speaking this linear way of describing interaction is inaccurate. It would be more correct to say that in earlier development - before differentiation of structures takes place - both "lower" and "higher" (and "higher" and "lower") stages interact in a very confused dynamic two-way fashion.
Then with later development of the more advanced stages, again "higher" and "lower" (and "lower" and "higher") dynamically interact in two-way fashion (this time in a mature manner). So from the nondual perspective, which fundamentally defines integration, we have no hierarchy.

6. Indeed I would be of the view - certainly when speaking of my own Roman Catholic tradition - that even its greatest saints rarely come fully to terms with the mythical manner in which its greatest truths are imparted.
For example the doctrine of the Virgin Birth, Christ's Resurrection, Transubstantiation of the Eucharist, the Immaculate Conception and the Assumption all relate to important spiritual truths that are conveyed in a somewhat mythical fashion. However because the early acceptance of these (in mythical terms) is used to define adherence to the tradition, it can subsequently be very difficult to appreciate these doctrines in a more universal fashion (where the bare universal truth is properly disentangled from its arbitrary mythical clothing).

7. I listened with interest some time ago on "Integral Naked" to Ken's so called reply to Mark Edward's criticism on this point. Of course as is so often customary in his responses, Ken does not actually deal with criticism in the context in which it is made but goes on something of a solo run with no direct relevance to the points that have actually been made.
Indeed I felt that - even in Ken's terms - his reply was somewhat vague and unsure lacking any real conviction or coherence. I strongly suspect that the underlying problem here is Ken's pre/trans fallacy, which is quite untenable from a dynamic interactive perspective.
To properly deal with the nature of childhood experience of the transpersonal (with respect to both its confused and nature expressions) we must clearly recognise the two-way dynamic links that necessarily exist between - what are referred to in discrete terms as - the prepersonal and transpersonal stages.
Now if Ken were to come right out in the open and do this, then it would raise serious questions with respect to his formulation of the pre/trans fallacy. So - perhaps at an unconscious level - he is hoping that by dealing with the matter in a somewhat vague manner, no one will notice the important problem that the issue poses for his formulation.

Incidentally I was amazed to hear in this reply Ken putting forth the view that (primary) states are mutually exclusive. Once again from a dynamic interactive perspective this is nonsense. Rather in this context all states (to a greater or lesser extent) are necessarily mutually inclusive of each other.

In support of this point, Ken again uses his dualistic mode of argumentation - which typifies in structural terms a merely differentiated approach to development - in stating that one must be either drunk or sober. This is quite untenable as there are various degrees possible with no clear dividing line therefore as between both states.
As I have said in the first note one could be moderately drunk yet still sufficiently awake to have an intelligent conversation. However, while in this state one might not yet be sufficiently awake (and thereby capable of exercising rational control) to drive a car safely. In other words the dream state (of a somewhat confused nature) can be induced to a degree by drinking that - when combined with waking - can significantly impair rational functioning with respect to some tasks (but not others). So when one is moderately drunk the waking and dream states are necessarily combined in various degrees. Then when one is very drunk the (confused) deep sleep state starts to intrude eventually culminating in a complete stupor.

8. Once again it is not truly possible in dynamic interactive terms to make a hierarchical distinction as between "lower" and "higher". More correctly we can have a confused expression of the two-way interaction of a "lower" with a "higher" (and a "higher" with a "lower") stage which typifies early (chronological) development; equally we can - with chronologically advanced spiritual development - have a mature experience of the this two-way interaction.

9. There was a fascinating episode in Ireland some 20 wars ago where large numbers of people testified to witnessing "moving statues" at various places of religious devotion throughout the country.
This could perhaps be explained in a time of rapidly changing values as a deep unconscious desire to recover some of the mystery associated with traditional forms of spiritual expression.
I would not doubt the sincerity of so many as to the accuracy of their observations that statues did indeed move. I would however explain this as a collective case of the "trance" like state where for a while the unconscious and conscious minds can overlap without the observer being able to discern as between both aspects. Strictly speaking people who witnessed "moving statues" were in fact "imagining" these events (through the operation of the unconscious) but as these images were projected into a consciously perceived environment these "imaginary" aspects could not be distinguished from the "real" (i.e. consciously perceived) events. Many others at the same venues did not notice anything unusual regarding the statues indicating that they were not sharing therefore in this collective "imaginary" trance.

10. The wave literally combines elements of the circle and line largely representing a circle that has been bisected and extended through time (representing the various phases of the wave cycle).